I know how to calculate the probability of rolling a 6 on a standard 6-sided die 3 times out of 3 etc. What I can't remember how to calculate is this:

If I were to roll TEN dice what is the probability that I would roll a 6 on:

a) EXACTLY 3 occasions
b) AT LEAST 3 occasions

If anybody can help me I would be grateful. Many thanks!

Sep 9th 2012, 03:06 AM

MarkFL

Re: Probability of 3 or more occurences out of 10

If I understand correctly, you are rolling 10 dice and you want to calculate the probability that:

a) exactly three 6's are showing.

b) at least three 6's are showing.

a) We need to know how many ways there are to choose 3 from 10:

We also need to know the probability of getting one particular set of 3 dice to show 6's:

Hence, the probability in question is:

b) Here, it will be simpler to calculate the probability of getting less than three 6's, i.e., to get 0, 1, or 2 6's, then subtract this from 1 (Do you understand why?). See if you can use the same technique outlined in part a) to find this probability.

Sep 9th 2012, 03:57 AM

CJ1969

Re: Probability of 3 or more occurences out of 10

Hi.

Thanks for that. Think it makes sense!

Cheers :)

Sep 9th 2012, 10:08 AM

Soroban

Re: Probability of 3 or more occurences out of 10

Hello, CJ1969!

Quote:

If I were to roll TEN dice, what is the probability that I would roll a 6 on: